IRJET- Brain Tumour Detection and ART Classification Technique in MR Brain Images using RPCA QT Decomposition

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 05 Issue: 04 | Apr-2018 www.irjet.net p-ISSN: 2395-0072
© 2018, IRJET | Impact Factor value: 6.171 | ISO 9001:2008 Certified Journal | Page 1717
Brain Tumour Detection and ART Classification Technique
in MR Brain Images using RPCA QT Decomposition
Padmanjali A Hagargi1, Dr.Shubhangi DC2
1Asst.Professor, Computer Science and Engineering GNDEC, Bidar, Karnataka, India
2Professor, CSE VTU PG Centre Kalburgi, Karnataka, India
---------------------------------------------------------------------***--------------------------------------------------------------------
Abstract: In medical field, image fusion is a significant
role to analyse the brain tumor which can able to classify
cancerous or noncancerous region. It is the method in which
many images are integrated to a similar view into single
fused image. This image is to decrease the uncertainty and
minimise the redundancy while extracting all the useful
information through the input source images. The image
fusion system is the combination of multi-images with
relative data into single image. This method can be used to
notice the brain tumor by combining T1 and T2 MRI slice
images. In this proposed method, an efficient image fusion
method using quad tree decomposition and robust principal
component analysis. Tumor segmentation is done using the
level set segmentation method. Then the feature extraction
is done with the complete local binary pattern approach and
pyramid HOG approach. ART classifier is also used to classify
the brain tumor to malignant or benign.
Key Words: MRI T1 and T2 Images, RPCA and QT based
Image Fusion, Level set Segmentation, CLBP and PHOG
Feature Extraction and ART Classifier.
1. INTRODUCTION
In medical field, image processing method has been
developing the significant factors where as in normal
medical applications is treatment planning and disease
diagnosis. Due to the scientific limits, the feature of the
medical-images is typically unacceptable; corrupting the
efficiency of the human interpretations and analysis of the
health images, needed a value of these images to improve
[01]. Now a day’s many of them facing the brain tumor
disease, this brain tumor can be group of growing an
abnormal cells in the head or brain. This is a cancerous or
noncancerous. Unlike another cancers, where cancer arise
starting from the brain tissues spreads rarely. All brain
tumor whether malignant or benign were serious. The
tumor grows eventually can compress also damage the
other format in the head. There is two varieties of brain
tumor such that primary tumor and secondary tumor. The
primary tumor will begin in the brain tissues and
secondary tumor spreads to the skull from other element
of the body.
Tumor analysis will play a critical role as detect the
size of the accuracy and position of brain tumor. The
medical science has seen a radical growth in biomedical
field analytical imaging. In present technologies in
computer vision and also artificial intelligence has been
effectively place into exercise in the applications are
diagnosis disease such that cancer by medical imaging. The
major important of the newest development in medical-
imaging are to be build more dependable and competent
algorithms are used diagnosis tumor in genuine time
purpose. Image fusion can appropriate a multi modality
images like computed tomography, position emission
tomography, magnetic resonance of the image and single
photon emission calculated tomography for recognition of
brain tumor. However, to identify the tumor different
image fusion approaches have developed.
Image fusion is divided into the three types such as pixel,
region, and decision level. It has two methods for pixel
stage like transform and spatial domain. Spatial domain
fusion techniques are easy and fused image which can be
achieved by apply the direct fusion rules on the source
image of the pixel values like averaging, principal
component analysis and linear fusion. However, the main
weakness of spatial domain will establish the spatial
distortion in fused images and does not supply any
information of spectral. Transform domain approach were
introduced to overcome the drawback of the fusion
method of spatial domain. The pyramid-based and wavelet
transform-based approach are mainly used for transform
domain method of the fusion [02].
In this paper, proposes a robust method of principal
component analysis with quad-tree decomposition based
algorithms for image fusion. These algorithms are takes as
an input is passed to feature extraction. Then extracted
images and fused those images to the tumor detection.
Pyramid histogram of the oriented gradient and also
complete local binary pattern techniques is used to feature
extraction of fused image. After extract the feature, this
will apply to the classification using ART classifier then
will get a malignant or benign image of brain tumor.
2. LITERATURE SUSRVEY
Zhenhua Guo et.al [03] has concluded modelling of
local binary pattern operator and also projected it. They
have analyzed a local binary pattern from point of vision,
also the local dissimilarity of the sign magnitude transform
and subsequently a novel method namely the CLBP.
Established sign element is much more significant than the
element of magnitude in reverse the local dissimilarity
data can describes the conventional LBP_S features would
be a more proficient than magnitude of CLBP features. At
last, through fusing the CLBP_M, CLBP_S and CLBP_C

codes, they could perform a best accuracy of the quality of
the organization than the state-of-arts LBP techniques.
Huilin Gao et.al [04] proposed an efficient algorithm
for image classification, on the basis of SVM and also fusion
of the multi feature. This process of the image feature
extraction and explanation are employing the integration
process of the pyramid histogram of color (PHOC),
pyramid histogram of words (PHOW) and pyramid
histogram of oriented gradient (PHOG). A Caltech 101
database is confirmed a validation of this projected
method for experimenting. Experimental outputs could be
see that accuracy rate of classifier approach is enhanced by
usual BOW approach.
Emmanuel J. et.al [05] proves that with some
appropriate considerations, it is possible to improve both
sparse and low rank components closely to solve very
convenient of convex program. They discuss a technique
for optimized problems and current applications in video
observation of the area. The projected scheme is allowed
to identify the objects in the background of the cluttered,
and face recognized area, to remove the shadows and
specularities in face images.
Atreyee sinha et.al [06] have proposed novel Gabor
based shape, color, local and texture feature extraction
approach encouraged by the pyramid HOG and fusing with
the GLBP features with an optimal feature of the
demonstration method. Such that PCA, to offer the GLP of
robust and also calculate its performance in six-various
color space and also in greyscale. By using three
impressive challenges of the datasets are demonstrate that
FC-GLP descriptor improve the presentation of the
organization in excess of the GPHOG and GLBP descriptors
and this can be successful when apply on the objects and
view the image classifiers are carried out.
Sugata Banerji N et.al [07] have presented on the
texture, color, wavelets and shape of the object and view of
the image-classification and also H-descriptor of feature
extraction can be developed by principal component
analysis method and enhanced fisher model. By fuse the
method of PCA feature of H-descriptor in seven-color
space will use further integrated the color data.
Experimental results were used 3 dataset, the Caltech 256
purpose category of the dataset, Scene MIT dataset and
Event dataset of UIUC Sports shows a projected novel
image descriptor accomplish a best presentation of image
classification than the admired image descriptors such
that are SIFT, PHOW, PHOG, C4CC, LBP, object bank and
hierarchical matching pursuit.
3. METHODOLOGY
The proposed scheme includes training and testing
phases. In training phase the segmented brain tumor
samples are applied in to pre-processing step. This pre-
processing step can used to resize the image, to convert an
image RGB to greyscale and remove the noisy by using
wiener filter. Then feature is extracted, once the pre
processing stage is done and extracted feature is stored in
knowledge base.
In testing phase two input sample images are given
to the pre-processing step. This step will remove the
unwanted noise and resize the input images also convert
the image RGB to greyscale, and then fuse the input images
by decomposition of the robust-principal component
analysis and the quad tree technique. Fused image is
subject to level set segmentation, and then an image is
segmented. Where segmented image is gives to feature
extraction. Extraction is used to extract the features of
image; complete local binary pattern with pyramid
histogram of oriented gradient process can apply to
feature extraction. Then feature extraction is subject to the
classification, ART classifier can be used here for final
resultant of an image. Then the proposed block diagram of
this paper is shows in Figure 1.
Figure 1 : Proposed Block diagram
3.1 Pre-processing:
This process can perform for filtered noisy; sharpen
the edge of an image and artifacts in the image. Also takes
place a conversion of RGB to gray and reshape the image.
It has a medium filter for removal of noise [08]. The skull
removing or stripping is complete by normalising an image
which can be fused and fill the inner area of an image. With
the use of maximum threshold, the mask process applied
to load the mask of image fuses the image which also
recovers the estimated original image with no portion of
the skull and also noise.
3.1.1 Wiener filter Method
The function of wiener has been derived from
wiener filter approach which can be a categorized the
linear filter. Apply this filter to an adaptive picture and
also adapt itself to a variance of local image. At the low
Image
Fusion
Training
Testing
Knowledge
Base
Brain Tumor
Classification
(Benign/Meligant)
Pre-processing
ART Classifier
Feature Extraction
Feature
Extraction
Segmented Tumor
Image Samples
Pre-
processing
Image 1
Image 2
· Resizing
· RGB to Grayscale
· Conversion
· Noise Removal (Wiener
Filter)
· Resizing
· RGB to Grayscale
· Conversion
· Noise Removal (Wiener
Filter)
· RPCA and QT
Decomposition
based Image Fusion.
· CLBP
· PHOG
Segmentation
· Level Set

variance the image will get equalized. Similarly it is
equalize the image more at high variance. Therefore this
wiener filter can provide a best result compare to linear
filter and also it’s perform is healthy where noise can be
constant power of the white noise additive is known as
Gaussian noise [09].
Wiener filter represents a coefficient of w vector,
is a input filtered signal, is produces a signal
output sample, this is establishing a least mean
square of desires otherwise target the signal of . The
correlation between input and the output signal sample of
a filter is shows in below equation 1,
In common,
Then discrete time index is representing with an m,
the sample input signal of the filter is shown as
, the vector
parameter of is gives a
coefficient vector of wiener filter. In beyond equation is
expressing the operation of filter into a two alternatives
also corresponding form of the convolution sum with the
profit of the inner vector. The signal error of wiener filter,
is define that the dissimilarity between a desired
signal of and the output sample signal of the
is given by,
Therefore error filter is given by,
Where above equation gives a desired signal
and an input sample signal , the error wiener filter
on the coefficient filter of the vector w. Then explore
the correlation between the signal error and filtered
coefficient of w vector and also expand the beyond
equation for the N number of sample signal. The
compressed notation of vector matrix can be given as,
Where x represents a desired signal, e gives an error
signal and Y is an input matrix signal. Then, final wiener
filtered output signal is as follows;
This will assuming an initial input sample signals
(P) can be known or else set
this to zero.
3.2 Image Fusion
In this part, we proposed the system on RPCA and
QT decomposition method. The two source input images of
the tumor are considered and are pre-processing. Then the
pre-processed images are fused by using decomposition
techniques as described below.
3.2.1 RPCA
Robust-principal component analysis is one of
decomposition based method, which can be proved an
effective mode to improve both sparse component and low
rank component. Closely from the higher dimension
information by determine a principal component of
pursuit. Where, the matrix of input information
has been subjected to the property of low rank. To recover
a structure low rank of D, D will be decomposed as,
Where, ‘E’ represents a spare matrix and ‘A’ represents
principle matrixes. This can be identified the problems to
solve the difficulty. Hence Wright has been demonstrating
when sparse matrix E is sufficient to spare, which can
accurately recovering a principal matrix of A from the
decomposed D while solving the optimal problem as
follows:
The is a parameter of the positive weighted,
represents a nuclear model of matrix A and is a first
norm of E matrix [10].
To solve the semi-definite program of robust the
PCA is having a possibility approaches. Interior point
process is suggest to the accurate and convergence of rate
[John Wright]. This method is used to solve, slight relax
version of equation (8), equal constraint is replace with
the penalty expression as shown below,
Where, is denoted as a small constant. This method is
minimizing a function by designing separable quadratic
approximation to an information term at
and is obviously select to achieve junction rate
of . Then those sub problems of the solution is
efficiently calculated by soft thresholding (E) and singular
threshold value.

Sub-gradient is having sufficient frobenius norm
which can be terminated in the form of iteration. The
convergence speed is radically improved via employing
the continuation strategy that can be started with the
relatively more and geometrically decreases at every
iteration until it reach a lesser bound.
3.2.2 QT Decomposition
Quad tree is an important data construction
whereas in each node, leaf is not having children in the
tree and single internal node is having exact four children.
This decomposition is the technique which can analysis
the partition of image to the block that will be large
homogenous than that image. In the traditional
decomposition quad tree of square image is partition into
a four equivalent size of an image and also block will
evaluating with certain threshold conditions of the
homogeneity sector. Where the block will meet the
threshold circumstances that do not sub divide into
further, while block will not meet the threshold
circumstances can be sub divide into a block of four. Then
that blocks will be evaluated by repeating iterative until
meet the threshold circumstances.
The complete image can represent the source node
where it is separated into four blocks and the homogeneity
will not meets the threshold circumstances. Therefore the
homogeneity block image will meet the threshold a
circumstance is representing with a leaf node. is a level
0 image. Then the first part related into
a sector of level 1. In level 1, the level0 and level3 blocks of
and can sub divide into a lesser blocks and are
and at second level.
In decomposition of quad tree rule, and
were later subdivided once they meet the threshold
circumstances [10]. Similarly the next step will also be
subdivided. In the scheme of the quad tree decomposition,
first division will perform based on lowest resolution
image then the sub division will perform based on the
highest image resolution. This can proved as the
decomposition having an advantage of the self adaptation
with high speed.
3.3 LEVEL SET SEGMENTATION
The segmentation of level set is presented by osher
and sethian for face propagation and can apply to the
blurry frames and ocean waves. Malladi applied, this level
set to medical imaging field. We describe the boundary
segmentation as section of surface where the formed level
is zero that known as zero level set. Where, correspond
to the contained surface as shown below,
Where denotes the position of our image, t
represents a time and d denotes the distance between
level set zero and position. If is level set zero outer, d
represents the positive values otherwise it gives a negative
sign. Let mark the curve by the location when , to
the more than time by the chain rule is as given below:
Consider where the vector normal (n)
in the front by the x point and s is several arbitrary vectors.
Therefore the s and n describes the complete field of x, in
fact those are the real vector domains. Then, this can be
written as;
Therefore, and s are representing a two forces which
are independent that will progress the surface, where
is a scalar vector. The scalar vector of will manage how
the surface can faster and shift in regular direction. The s
vector can be the other force that dictates in both
directions and growth of speed. Then, equation of
incomplete differentiation can solve the primary condition
. Since, the segmentation will get reduce into
the initial value to solve a problem.
3.4 FEATURE EXTRACTION
After segmenting an image, it can be subject to the
feature extraction. This extraction is carried out with the
CLBP and pyramid histogram of the oriented gradient
methods, explained as follows.

3.3.1 Complete Local Binary Pattern (CLBP):
The CLBP defines a complete local binary pattern.
This is used to improve an effective texture analysis. The
complete local binary pattern will representing a local area
with central pixel and differentiated among the values by
the central local pixel with the magnitude is known as
difference sign magnitudes transform and it denotes as
LDSMT. Figure 2 represents a general flow chart of
complete local binary pattern. The CLBP is having a three
various mechanisms such as CLBP-S, CLBP-M and CLBP-C.
Whereas the CLBP-S illustrates the sign values like positive
or negative differences among a local pixel and centre
pixel. CLBP-M gives dissimilarity among the magnitude of
centre pixel and local pixel. CLBP-C implies the difference
among the average central pixel and local pixel values.
CLBP-S is a normal LBP as follows,
CLBP-M is calculated and is as similar as the CLBP_S,
but this will contract with the magnitude differences as
shown as,
Then the threshold is to be resolved adaptively with
the magnitude component. The centre image pixel is
having a discriminate data. The CPBP_C [11] is as follows;
The equation 21 defines the threshold to compute
the average gray level of complete the image.
Figure 2 : Flow Chart of CLBP
3.3.2 Pyramid Histogram of oriented Gradient
(PHOG)
HOG is proposed for the pedestrian identification in
the static videos or the images. The approach will count
the amount of times; the oriented gradient is arrived in
local images. Therefore it is an effective process to explain
the shape which is having the information of an image.
The data allocation of the gradient or edges is
extracted only for the local area of the image that is best
characterization of an arrangement that supposed to be an
edge or the gradient of an object in local region. Therefore
it achieves to show the shape of an object. Initially the
complete image has to segment the image into dense grid
of the consistent where the spaced cell and gradient path
will divide in to K bins. Therefore all pixels of the gradient
in any cell can be calculated to generate an oriented
gradient which can be measured as K-dimension feature
vector into a model of descriptor for each cell. Finally, all
cells of the oriented gradient descriptor will
interconnecting to represents the vector feature of sub
images. The histogram of an oriented gradient is having a
better robustness beside the illustration and also changes
in geometric.
Histogram of oriented gradient is measured as the
spatial distribution image information, but it will not take
a description on classification performance that causes a
Fused image
Fuse image
Fused image divided into
several blocks
Histrogram calculated for
each block
Block CLBP histogram are
concentrated into
Fused image represented
by CLBP
No
Yes

spatial scale division in different directions of an images.
Since the Bosch proposes a shape feature that describes
both the spatial with local image and is known as the
Pyramid histogram of oriented gradient.
Initially an image is needed to generate a pyramid
image which can be hierarchically partitioning to quad tree
of the multiple stages of sub blocks. Then, extract a feature
of HOG from each cell in each levels of the pyramid image.
Then combine the multilevel HOG of various stages from
the lowest resolution to highest resolution to form the
image feature of the PHOG. To explain the shape and edge
of the image for the PHOG with the increase of the
partition stages is more refining and localized.
Algorithm steps for Pyramid Histogram of Oriented
Gradient:
Step.1. Initially, the pyramid of the hierarchical
images has built for the grid partitioned.
Step.2. Source images are partitioned the
hierarchical form to multistage sub blocks of
the quad tree.
Step.3. By edge detection, algorithm is extracting the
contour edge of images into every partition
level.
Step.4. Compute the gradient way, amplitude of
every pixel edges and also the gradient scope
direction is [0,360] or [0,180] this is
separated into k-intervals.
Consider the number of pixels of the gradient direction
will get the values in each interval. The gradient
amplitude of every pixels in every interval of weight will
corresponds to an interval that can be represents the
gradient ways of histogram as shown below,
Histogram of the all partition levels of the images
are normalised, those normalised weight of the HOG in l th
stages is . Successively, concentrate on those
histograms to achieve the final shape of pyramid of HOG
description of the histograms.
3.5 ART Classifier
ART defines an adaptive resonance theory will build
decision tree and can be used greedy algorithm but every
decision should not revoke at once. Therefore this can
employ an association-rule of mining algorithm to
powerfully construct partial classification models and also
it has a requirement of the typical user. The specified
thresholds are using in minimum support for frequent
item-sets, association mining rule and association of
minimum confidence rule. In this theory min-support
threshold gives a percentage of present size of the data set
and it inhibits the factor of the branch tree. Since, the
primary keys or student keys in input of dataset do not
selected with ART.
4. EXPERIMENTAL RESULTS
The result is done by the database of the dataset.
Initially pre-processing step is done by the conversion of
RGB to greyscale and filtered, then fusing this filtered
image by using RPCA and QT technique. The fuse image
provides the level set segmentation. Then segment image
can extract the feature by the ART classification; finally
will get the detection of tumor in a brain image that is
malignant or benign. The figure 3, figure 4, will gives a
complete dataset of the brain tumor detection. The Figure
3 (a) and (b) shows an input two images and once pre-
processing is done, will get filtered images is shown in
figure (c) and (d). Figure (e) will give a fuse image with the
help of RPCA and QT decomposition method. Then fusing
an images to get the segmented images is shows in figure
(f) and figure (h) is the tumor segmented image, then
checks the detection of brain tumor image and gives
information either it is malignant or benign that is shows
in (i).
Similarly, in Figure 4 same functional steps are
repeated with another datasets. In which each functional
output of corresponding given dataset is pictorially
presented.
(a) (b) (c) (d) (e)
(f) (g) (h) (i)
Figure 3: (a) Input T1 Image (b) Input T2 Image (c)
Filtered T1 Image (d) Filtered T2 Image (e)198 Iterations
in Fuse Image (f) Level Set Segmented Image (g)
Segmented Tumor Parts (h) Validated Tumor Part (i)
Selected Region of Tumor
The segmentation of level set algorithm endure 200
iterations to find the tumor region part is shows in (f) and
finally gives an output of it shows in (g). This segmented

region can be whether malignant or benign, therefore it
detects the feature extraction of brain tumor is using a
technique of CLBP and PHOG then it passes to the ART
classifier to classify either it can be malignant or benign.
The detected area is shows in (i)
The algorithm is evaluated on various MRI images
consisting of tumor regions. Experiments gives that the
projected system gives better results when compared than
the previous systems.
(a) (b) (c) (d) (e)
(f) (g) (h) (i)
Figure 4 : (a) Input T1 Image (b) Input T2 Image (c)
Filtered T1 Image (d) Filtered T2 Image (e)198 Iterations
in Fuse Image (f) Level Set Segmented Image (g)
Segmented Tumor Parts (h) Validated Tumor Part (i)
Selected Region Of Tumor (j) Detection either Malignant or
Benign
The evaluation metrics of accuracy, precision,
sensitivity, specificity and recall are assured in terms of
the , , and . Sensitivity is the ratio of true positives
that can be correctly recognized with the analytic trial. It
denoted that how the test image is detecting a disease.
The Specificity defined as the ratio of true negatives
exactly recognized with the analytic trial. It denoted that
how best the test is detecting normal (negative) case.
Accuracy can be defines as the ratio of true results, either
true negative or true positive, in a population. It can
evaluate degree of the veracity of analytic test on the
shape.
The Precision and recall formula is shows in below,
Table 1 : Proposed Confusion Matrix
Total
Dataset 1 24 12 1 1 38
Dataset 2 20 11 1 1 33
Dataset 3 23 9 1 1 34
Dataset 4 19 13 1 1 34
Dataset 5 28 11 1 1 41
Total 114 56 5 5 180
Table 2 : Different datasets for the
Accura
cy (%)
Precisio
n (%)
Sensitivi
ty (%)
Specifici
ty (%)
Reca
ll
(%)
Data
set 1
94.73 96 96 92.30 96
Data
set 2
93.93 95.23 95.23 91.6
95.2
3
Data
set 3
94.11 95 95.83 90
95.8
3
Data
set 4
94.11 95 95 92.85 95
Data
set 5
95.12 96.55 96.55 91.66
96.5
5
Averag
e
94.4 95.55 95.72 91.682
95.7
2
Table 3: Comparison table for proposed and existing
method of Accuracy
Paper Year Methods
Accuracy
(%)
Comparative
Analysis of
Classifier
Performance on
MR Brain Images
[12]
2015
Association Rule
(AR) based NN
classifier
83.7
Brain Tumor
Detection Using
Hybrid Techniques
and Support
Vector Machine
[13]
2015
C-means
Segmentation
algorithm
88
Implementation of 2016 Adaptive K- 88.67

Clustering
Techniques For
Brain Tumor
Detection [14]
clustering
Gender
classification from
an iris images by
using uniform LBP
fusion [15]
2010 Histogram LBP 91.33
Brain Tumor
Detection Using
Image
Segmentation [16]
2016
Particle Swarm
Optimization
92.8
Proposed Method 2018
RPCA + Quad
tree
Decomposition +
CLBP, PHOG+
ART
94.4
Table 4: Comparison table for proposed and existing
methods of Sensitivity and Specificity
Paper
Yea
r
Method
Sensitivi
ty (%)
Specifici
ty (%)
Comparativ
e Analysis
of Classifier
Performanc
e on MR
Brain
Images [12]
201
5
Association
Rule (AR)
based NN
classifier
90.27 88
Analysis
And
Evaluation
Of Brain
Tumor
Detection
From MRI
Using F-
PSO And
FB-K
Means [17]
201
6
Fuzzy
Bisector K-
means
clustering
77 80
MRI Brain
Image
Segmentati
on Using
Combined
Fuzzy Logic
and Neural
Networks
for Tumor
Detection
[18]
201
3
Level Set,
Neural
Networks,
Fuzzy logic
94 93
Proposed
Method
201
8
RPCA +
Quad tree
Decompositi
on + CLBP,
PHOG+ ART
95.72 93.682
Table 3, Table 4 represents the comparison for the
proposed systems and the existing systems and this gives
that proposed system has better results when compared
than the previous systems with accuracy, sensitivity and
specificity of 94.44%, 91.68%, 95.72% and respectively.
Figure 5 and Figure 6 shows the comparison graph of the
previous system with proposed method of accuracy,
sensitivity and specificity.
Figure 5: Comparison graph for Accuracy
Figure 6: Comparison graph for Sensitivity and Specificity
CONCLUSIONS
In this work, we proposed the technique for the
detection of tumor is using a fusion process on the robust
principal component analysis, quad tree decomposition
and ART classifier that will detect the brain tumor part.
Before applying the ART classifier the fuse image will get
extracted. The Complete local binary pattern and pyramid
HOG approach can be extract the feature. Finally obtaining
the cancerous or non cancerous brain images, this
provides a better accuracy than the previous methods.

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